Half Heusler Research Articles

Synthesis and Thermoelectric Properties of ZrxTi1−xNiSn0.98Sb0.02 n-Type Half-Heusler Materials

Hf-free ZrxTi1−xNiSn0.98Sb0.02 (x = 0.25, 0.5, 0.75) n-type half-Heusler (HH) thermoelectric materials were synthesized by a serial processing method including induction melting (IM), annealing, ball milling, and spark plasma sintering (SPS). For comparison, a Hf-containing half-Heusler Hf0.25Zr0.25Ti0.5NiSn0.98Sb0.02 ingot was also alloyed by arc melting, and the effects of Hf on the thermoelectric properties were estimated. The ZrxTi1−xNiSn0.98Sb0.02 HH materials were nearly pure according to the x-ray diffraction analysis, but microscopic investigation revealed impurity phase inclusions of unalloyed Sn, Zr, and Ti. The power factor (PF) of the Hf-free HH materials reached the maximum value of 4.31 mWm−1 K−2 at 823 K in Zr0.75Ti0.25NiSn0.98Sb0.02, which was higher than Hf0.25Zr0.25Ti0.5NiSn0.98Sb0.02 (4.01 mWm−1 K−2 at 773 K) in this study. However, the thermal conductivity of the Hf-free samples was significantly higher, by which the maximum dimensionless figure of merit was slightly lower (ZTmax = 0.92 in Zr0.75Ti0.25NiSn0.98Sb0.02 at 873 K) than that of Hf0.25Zr0.25Ti0.5NiSn0.98Sb0.02 (ZTmax = 1.03 at 873 K). The thermal conductivity was decomposed into lattice and electronic contributions, and the possible correlation with Ni off-stoichiometry is discussed.

Thermal properties of TiNiSn and VFeSb half-Heusler thermoelectrics from synchrotron x-ray powder diffraction

Half-Heusler (HH) alloys are an important class of thermoelectric materials that combine promising performance with good engineering properties. This manuscript reports a variable temperature synchrotron x-ray diffraction study of several TiNiSn- and VFeSb-based HH alloys. A Debye model was found to capture the main trends in thermal expansion and atomic displacement parameters. The linear thermal expansion coefficient α(T) of the TiNiSn-based samples was found to be independent of alloying or presence of Cu interstitials with α av = 10.1 × 10−6 K−1 between 400 and 848 K. The α(T) of VFeSb and TiNiSn are well-matched, but NbFeSb has a reduced α av = 8.9 × 10−6 K−1, caused by a stiffer lattice structure. This is confirmed by analysis of the Debye temperatures, which indicate significantly larger bond force constants for all atomic sites in NbFeSb. This work also reveals substantial amounts of Fe interstitials in VFeSb, whilst these are absent for NbFeSb. The Fe interstitials are linked to low thermal conductivities, but also reduce the bandgap and lower the onset of thermal bipolar transport.

High entropy alloy on single sub-lattice in MNiSn compound: Stability and thermoelectric properties

Half-Heusler (HH) High entropy alloy (HEA) MNiSn (M=Ti,Zr,Hf) with addition of Al and Sc in the M sub-lattice was studied. The micro-structure of (Ti0.33Zr0.33Hf0.33Al0.005Sc0.005)NiSn compound was examined and its transport properties were measured. The measurements showed the improvement of ~40% in the thermoelectric figure of merit in comparison with a similar composition of (Ti0.3Zr0.35Hf0.35)NiSn without Al and Sc. The thermodynamic stability of the alloy was examined using the HEA methodology, including a new proposed HEA parameter for multi-component alloying in only one sub-lattice of the compound. Ab-initio density functional theory (DFT) calculations were carried out to obtain the binary interaction parameters between the components in the sub-lattice of M atoms. The thermodynamic stability of the alloy as a function of the atomic fraction of the elements occupying the same sub-lattice in the compound is analyzed using the new HEA parameter.

Structural stability and thermoelectric properties of new discovered half-Heusler KLaX (X = C, Si, Ge, and Sn) compounds

Structural, elastic, electronic, and thermoelectric properties of KLaX (X = C, Si, Ge and Sn) half Heusler compounds have been studied using the full potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). It is shown that the KLaX half Heusler compounds are energetically and mechanically stable. The calculated band structure estimates with modified Becke-Johnson (mBJ) potential, indicates a semiconducting nature with direct band gaps of 0.76 eV, 0.79 eV, and 0.81 eV for KLaC, KLaSn, and KLaX (X = Si and Ge) respectively. The valence band of KLaX is more influenced by spin-orbit coupling than in the conduction band. The Seebeck coefficient (S), electronic conductivity (σ), electronic thermal conductivity (κe), figure of merit (ZT) and the power factor (PF) have been investigated using the semi-classical Boltzmann transport theory with rigid band theory. The KLaX half Heusler compounds exhibit high thermopower values and p-type charge carriers for their thermoelectric performance than electron doping. Including the spin-orbit coupling in our calculations increases the flatness of the valence band from X = Si to Sn. The high values of ZT and PF of KLaX half-Heusler compounds make it promising materials for thermoelectric applications.

Top-down method to fabricate TiNi1+xSn half-Heusler alloy with high thermoelectric performance

The top-down method was used to fabricate the TiNi1+xSn half-Heusler alloy. Several knotty problems have been solved using the top-down method, including the generation of impurity phases, the visible discrepancy in the grain size of the TiNi2Sn second phase, and irregular variations in the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ) with increasing Ni content. The generation of a large number of incoherent interfaces between the half-Heusler (HH) and full-Heusler (FH) phases fabricated by the top-down method drastically improved σ and retained κ and S, thereby leading to an enhancement in the dimensionless figure of merit (ZT) by ∼19 % for the TiNi1.05Sn sample as compared to the ZT of the samples prepared by the conventional method.

High Thermoelectric Performance in n-Type Degenerate ZrNiSn-Based Half-Heusler Alloys Driven by Enhanced Weighted Mobility and Lattice Anharmonicity

ZrNiSn-based half-Heusler (HH) alloys are well-established alloys for n-type mid-temperature thermoelectric applications because of their chemical and thermal stability and narrow band gap driven s...

Theoretical investigation of novel half Heusler compounds MRhSb (M = Nb & Ta): For optoelectronic and thermoelectric applications

AbstractThe main objective of this work is to make a detailed study on a new class of half heuslers which possess a 19 valence electron and which are sought for perpetually because of their thermoelectric performances. The mechanical, electronic structures, optical, and electrical transport properties are studied using full potential linearized augmented plane wave (LAPW) + local orbitals (lo) scheme, in the framework of density functional theory (DFT) with generalized gradient approximation (GGA) for the purpose of exchange correlation energy functional. The electronic structure is treated by the TB‐mBJ exchange‐correlation potentials. The independent elastic constants and the related mechanical properties are investigated. From the energy bands and density of states it is observed that the 3d‐states of Nb, Ta, and Rh atoms contribute mainly to the conduction band, which results in increase in electrical and thermal conductivity of NbRhSb and TaRhSb . The optical constants as the dielectric function, refractive index, optical reflectivity, and absorption coefficient were calculated and discussed in detail. The dependence of Seebeck coefficient, electrical conductivity, and power factor on the Fermi level is investigated.

Theoretical study of thermo-dynamical and thermoelectric properties of novel half-Heusler alloys AlNiAs and AlNiSb

In the present report, the investigation related to the thermodynamical properties of both half-Heusler (HH) alloys ‘AlNiAs’ and ‘AlNiSb’ have been made under the framework of Density Functional Theory (DFT) by implementing quasi-harmonic approximations. The calculated value of Debye temperature for AlNiAs (ΘD = 344.890 K) is higher than that for AlNiSb (ΘD = 309.211 K). In addition to the thermodynamical properties, the thermoelectric properties are also explored by utilizing the semi-classical Boltzmann transport theory by combining it with DFT. The variation of thermoelectric parameters such as the Seebeck coefficient, electrical conductivity, power factor, and electronic thermal conductivity with chemical potential, temperature, and doping concentrations are investigated for the first time. Both HH alloys AlNiX (X = As and Sb) have a negative Seebeck coefficient, which indicates their n-type behavior. It is concluded from the present study that ‘AlNiSb’ is a more admirable thermoelectric material than ‘AlNiAs’ over the temperature range from 50 K to 800 K.

First principles computation of structural, electronic, magnetic and mechanical properties of new lithium based half Heusler alloys

First principles calculations have been accomplished for structural, electronic, magnetic and mechanical properties of half Heusler (HH) LiYZ ([Formula: see text], Rh and [Formula: see text], Se, Te, Sb) alloys using the density functional theory (DFT) within full potential-linearized augmented plane wave (FP-LAPW) method. To calculate the physical properties, Perdew–Burke–Ernzerhof (PBE) potential and generalized gradient approximation (GGA) are employed. The calculations are accomplished for three phases to obtain the most stable phase. The results of these calculations revealed that Type-III is the most stable of LiRhSe and LiRhSb, Type-I of LiRhAs, LiRhTe, LiRuAs, LiRuSb, LiRuSe and LiRuTe alloys. The structural optimization is obtained by plotting the graphs between minimum volume and the lowest energy of all considered alloys. The results of electronic properties including density of states (DOS) and band structures are also presented. The obtained total magnetic moment (MM) is negative for LiRhSb, LiRuSb, LiRhTe, LiRuTe, while it is positive for LiRhSe, LiRuSe, LiRhAs, LiRuAs Heusler alloys (HAs). To determine the mechanical stability, several parameters such as Poisson’s ratio, Pugh’s ratio, Lame’s coefficient, anisotropy factor, Kleinman parameter, Young’s modulus, Bulk modulus and Cauchy pressure are calculated and discussed in detail.

Ruthenium-based half Heusler alloys RuTiX (X = Si, Ge, Sn): An FP-LAPW-based analytical study of structural, electronic, elastic, mechanical and transport properties

An full potential linearized augmented plane wave (FP-LAPW)-based analytical study of structural, electronic, mechanical and thermoelectric properties has been done for the Ruthenium-based half heusler RuTiX (X = Si, Ge and Sn) compounds. An efficient method to develop Half Heusler (HH) alloys is by examining their stability of structure in various phases, by plotting electronic band structures, computing elastic constants and also by studying the presence of magnetic moments. In this study, we have used DFT-based calculations to scrutinise the paramagnetic/ferromagnetic (FM) as well as metallic/semiconducting behavior of these HH compounds. The predicted phase stability using the energy versus volume curves reveals that they are stable in Type C phase. RuTiSi and RuTiGe are found to be stable in the paramagnetic phase whereas RuTiSn is stable in the FM phase with a finite value of magnetic moment. The electronic band structures and density of states (DOS) plots predict that the studied compounds belong to [Formula: see text]-type degenerate semiconductors as the Fermi Level lies within the valence band. Due to the existence of finite DOS at the Fermi level, they show an enhanced metallic behavior. A small value indirect gap is found between valence band maximum (VBM) and conduction band minimum (CBM) in all these studied RuTiX HH alloys depicting their semiconducting nature. The elastic constants of cubic phase are computed for the first time and they obey the mechanical stability criteria. The positive value of [Formula: see text] and value of [Formula: see text]/[Formula: see text] ratio of these HH compounds exhibit their ductile nature. The thermoelectric properties of these compounds are investigated, and a comparatively higher figure of merit reveals their scope of application in thermoelectric devices.

Structural, electronic and thermoelectric performance of narrow gap LuNiSb half Heusler compound: Potential thermoelectric material

We report the band structure calculations of rare earth based half Heusler LuNiSb compound for thermoelectric performance. A narrow energy gap of 0.227 eV is opened using TB-mBJ approximation. The value of Seebeck coefficient 288 (μVK −1) at room temperature using mBJ scheme is quite large as compared to the experiment as well as well known thermoelectric material PbTe at same temperature. The observed highest value (6.1 × 10 10 Wm −1 K −2 s −1) at 647 K is close to our calculated value 9.93 × 10 10 Wm −1 K −2 s −1 at 650 K using GGA + U approximations. We found the Lu-4 f flat bands lie in conduction band along Γ– X direction are mainly responsible for maximum peaks of Power factor. The high value 0.804 of ZT and value of other thermoelectric parameters indicate that LuNiSb would be a favourable material for room temperature thermo electric applications.

First principle computation of half metallicity and mechanical properties of a new series of half Heusler alloys KMnZ (Z = B, Si, Ge, As) for spintronics

In the framework of density functional theory, the first principle calculations are performed to investigate various physical properties of new series of half Heusler alloys KMnZ (Z = B, Si, Ge, As) by using WIEN2k code. The results of structural parameters show that ferromagnetic state is more stable, with Type 3, configuration than the non-magnetic and antiferromagnetic states for all KMnZ (Z = B, Si, Ge, As) compounds. All considered alloys KMnZ (Z = B, Si, Ge, As) are completely spin polarized and show half-metallic character because of the presence of band gap (BG) in minority-spin channels. The calculated magnetic moments are 3 µB, 4 µB, and 5 µB for KMnB, KMnSi (Ge), and KMnAs, respectively. The values of minority BG for KMnB, KMnSi, KMnGe, and KMnAs are 0.60 eV, 0.85 eV, 1.00 eV, and 1.20 eV, respectively. The origin of their HM gaps is also examined in addition to density of states and band structures. The Curie temperature (TC), within mean field approximation, is also calculated. The calculations for elastic constants and other mechanical parameters are computed to check the mechanical stability which revealed that all other alloys are stable with ductile nature except KMnB. From the results of several physical properties, it can be envisaged that these materials can be used for spintronic devices.

A Computational Investigation on Structural, Mechanical, Electronic, Magnetic, Thermoelectric, and Optical Properties of CrXPb (X = Sc, Ti) Half-Heusler Alloys

We have performed a broad computational study of two half-Heusler (HH) alloys CrXPb (X = Sc, Ti) by systematically investigating their structural, mechanical, electronic, magnetic, thermoelectric, and optical properties by means of spin polarized ab initio simulations using density functional theory. Their relaxed structures indicated that they attain cubic structure in ground state. We have used PBE-GGA method for optimizations and for attaining the most accurate results of all properties, the mBJ-GGA approach is applied. Both these compounds are ductile in nature and have anisotropic elastic behavior and high stiffness. CrScPb is observed to acquire metallic nature for both spins, whereas CrTiPb is observed to have half-metallic nature (narrow band gap of 0.96 eV) with a magnetic moment of 5 μB and 4 μB for CrScPb and CrTiPb respectively. Furthermore, the thermoelectric properties showed that CrScPb has comparable but better quantity of figure of merit (ZT~0.25 for spin-up and ~ 0.5 for spin-down at room temperature) for both spins and CrTiPb has improved response for spin-up, since ZT is close to 1 at room temperature. Such values showed the efficiency of these alloys for energy conversion and power generation. Moreover, the optical properties showed variable and remarkable optical behavior in visible and UV ranges. We observed fascinating optical applications such as energy storage, reshaping of phases in optical antennas and magentaoptical devices. In nutshell, we comprehend the various properties of two potential HH alloys targeting for various applications.

Investigation on Electronic and Thermoelectric Properties of (P, As, Sb) Doped ZrCoBi

Since the last decade, the half-Heusler (HH) compounds have taken an important place in the field of the condensed matter physics research. The multiplicity of substitutions of transition elements at the crystallographic sites X, Y and (III-V) elements at the Z sites, gives to the HH alloys a multitudes of remarkable properties. In the present study, we examined the structural, electronic and thermoelectric properties of ZrCoBi0.75Z0.25 (Z = P, As, Sb) using density functional theory (DFT). The computations have been done parallel to the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. The thermoelectrically properties were predicted via the semi-classical Boltzmann transport theory, as performed in Boltztrap code. The obtained results for the band structure and densities of states confirm the semiconductor (SC) nature of the three compounds with an indirect band gap, which is around 1eV. The main thermoelectric parameters such as Seebeck coefficient, thermal conductivity, electrical conductivity and figure of merit were estimated for temperatures ranging from zero to 1200K. The positive values of Seebeck coefficient (S) confirm that the ZrCoBi0.75Z0.25 (x = 0 and 0.25) are a p-type SC. At the ambient temperature, ZrCoBi0.75P0.25 exhibit the large S value of 289 µV/K, which constitutes an improvement of 22% than the undoped ZrCoBi, and show also a reduction of 54% in thermal conductivity (κ/τ). The undoped ZrCoBi has the lowest ZT value at all temperatures and by substituting bismuth atom by one of the sp elements (P, As, Sb), a simultaneous improvement in κ/τ and S have led to maximum figure of merit (ZT) values of about 0.84 obtained at 1200 K for the three-doped compounds.

Outstanding Thermoelectric Performance Of N-Type Half-Heusler V(Fe <sub>1-X</sub> Co <sub>x</sub>)Sb Compounds at Room-Temperature

The effects of cobalt substitution at the Fe-site on the crystal structure, electronic structure and thermoelectric (TE) properties of half-Heusler (HH) V(Fe1-X Cox)Sb compounds are investigated. Crystal structural analysis using powder X-ray diffraction clarified that all compounds have deficient HH structures (Huang et al., Chem. Mater., 32, 5173-5181, 2020). With Co-substitution at the Fe 4c sites, defects are observed in the V 4a and Fe 4c sites, and a small amount of Fe atoms enter into 4d sites, which is normally vacant in an ideal HH structure. The deficient HH structures of the V(Fe1-X Cox)Sb compounds are supported by electronic structural analysis using the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA). All compounds exhibit n-type behavior in both calculations and experiments with deficient HH structures. The absolute value of the Seebeck coefficient |S|, decreases with an increase in the cobalt content x . The tendency of the experimental |S| value to decrease corresponds well with the |S| determined by KKR-CPA calculations. Cobalt substitution acts as an electron dopant that effectively tunes the carrier concentration. The optimized carrier concentration of 2.1×1020 cm-3 leads to the highest power factor of 5.7×10-3 W/K2 m at room temperature for the V(Fe 0.99Co0.01)Sb compound. The V(Fe1-X Cox)Sb compounds are thus potential candidates as n-type TE materials for power generation near room temperature.

Electronic structure and optical properties of Rare-Earth based ErPdSb half Heusler Compound: A GGA + U study

Abstract The electronic and optical properties of rare-earth based half-Heusler ErPdSb compound are investigated by the using of first-principle density functional theory. The generalized gradient approximation (GGA) with spin–orbit coupling (SOC) and Hubbard parameter (U) have been used for exchange and correlation effect. Our calculations of electronic band structure show the half metallic nature of ErPdSb compound. The majority spin (up) states found semiconductor nature with a narrow indirect band gap 0.25 eV. While minority spin (down) states found metallic with no gap. The optical properties are investigated via optical conductivity, reflectivity along with other related optical constants such as absorption coefficient and refractive index.

Electronic Structure and Thermoelectric Performance of Narrow‐Gap GdNiSb Half Heusler Compound: Density Functional Calculations

The rare earth‐based half Heusler GdNiSb compound is investigated theoretically for electronic and thermoelectric (TE) performance. The most efficient method to treat the rare earth metals, Coulomb‐corrected local spin density approximation (LSDA + U), is used. The calculated total density of states (DOS) of GdNiSb shows that the maximum contribution near Fermi energy (EF) is due to the spin‐up/down Ni‐3d and spin‐down Gd‐4f states. A narrow energy gap of 0.279 eV is opened which is consistent with other reported values. TE properties are investigated using classical transport theory. The total Seebeck coefficient (S) increases linearly with temperature and attains a maximum value of 80 μV K−1 at 800 K. The S value of 60 μV K−1 at 380 K is in good agreement with the experimental value, 58 μV K−1, at the same temperature. The maximum value of the power factor (P) is as high as 825 × 109 W m−1 K−2 s−1 at 650 K in the spin‐down channel. The TE figure of merit (ZT) reaches the maximum value of ≈0.475 at 800 K in the spin‐down configuration. All the values of the TE parameters of GdNiSb indicate a good candidate for TE applications.

First-principles investigation on the thermoelectric performance of half-Heusler compound CuLiX(X = Se, Te)

The remarkable thermoelectric performance is predicted for half-Heusler (HH) compounds of CuLiX (X = Se, Te) based on the first-principles calculation, the deformation potential (DP) theory, and semi-classical Boltzmann theory. The Slack model is employed to evaluate the lattice thermal conductivity and the result is in good agreement with the previously reported data. The results of mechanical properties demonstrate that CuLiSe is ductile but CuLiTe is brittle. The relaxation time and the carrier mobility are calculated with DP theory. The electrical and thermal conductivities are obtained by using the semi-classical Boltzmann theory based on the relaxation approximation. The Seebeck coefficient and power factor are obtained and their characters are analyzed. The dimensionless figure of merits (ZT) is obtained for the p- and n-type CuLiX. The maximum ZT of 2.65 can be achieved for n-type CuLiTe at the carrier concentration of 3.19 × 1019 cm−3 and 900 K, which indicates that this compound is a very promising candidate for the highly efficient thermoelectric materials.

Exploring the electronic fitness function, effective mass, elastic and transport properties of RhTiP Half-Heusler alloy

Half Heusler alloys are among the most studied materials because of their high performance as thermoelectric materials. In view of this, we present ab-initio electronic and thermoelectric properties of RhTiP. In this work, DFT-GGA(PBEsol) was used to obtained lattice constant and electronic band structure and Elastic properties. Semi-classical Boltzmann theory was used to obtain the Seebeck coefficient, electrical conductivity, power factor, and electronic fitness function. The lattice constant of RhTiP is 5.69Å, and the band structure shows that RhTiP has an indirect bandgap of 0.83 eV. The Elastic properties predict the mechanical stability of RhTiP. The Seebeck coefficient of 368.23 μV/K and power factor of 0.51 mW/mK2 at 800 K are obtained from this calculation, Electronic Fitness Function of 1.13 is obtained at 800 K. From our results, it shows that RhTiP is a good thermoelectric material.

How Severe Plastic Deformation Changes the Mechanical Properties of Thermoelectric Skutterudites and Half Heusler Alloys

Thermoelectric leg materials with a high figure of merit, ZT, are the essential basis to build thermoelectric generators, directly converting waste heat into electricity. Skutterudites and half-Heusler alloys are promising candidates because they can be used in a wide temperature range, the starting material is available and cheap and in addition they are environmentally friendly. Severe plastic deformation via high-pressure torsion (HPT) is a technique to achieve very fine grains in micro- or even nano size with small and high angle grain boundaries and in parallel introduces a high level of defects like vacancies and dislocations. Therefore, this method was applied not only to enhance ZT of ball-milled and hot-pressed skutterudites and half-Heusler alloys but so far was also successful to directly produce dense nanostructured bulks from skutterudite powders. Although HPT compacted samples are chemically homogeneous, they are not homogeneous with respect to the shear strain increasing from the center to the rim. HPT changes the microstructure and density and thereby not only influences the thermoelectric but also the mechanical properties. In this work an overview is given of the influence of HPT on hardness, elastic moduli, indentation fracture toughness, thermal expansion and thermal shock resistance. The corresponding properties of hot-pressed skutterudites and half-Heusler alloys are compared with those after severe plastic deformation, dependent on the processing properties and position of the specimen in respect to shear strain. Data are collected from earlier investigations of the authors and from the literature, but also newly achieved and evaluated data are included.